The date for the conclave of cardinals to begin their deliberations has not yet been set, although one of Pope Benedict XVI's final acts before resigning his office was to amend the rules governing the election of a successor, allowing the cardinals to meet earlier than the usual 15-day transition between pontificates.

On Thursday, soon after Benedict left the Vatican on his final day as pope, Monsignor Carlo Maria Celli, a papal communications officer, hinted that the date could be March 11.

That could not be immediately confirmed.

The date of the conclave's start is important because Holy Week begins March 24, with Easter Sunday March 31. In order to have a new pope in place for the church's most solemn liturgical period, he would need to be installed by Sunday, March 17 -- a tight time frame if a conclave were to start March 15.

Cardinal Francis George, of the Archdiocese of Chicago, told CBS News he hopes the papal conclave will work quickly to name a new pope when it convenes next month -- but he does not know who he will vote for.

"Not yet, I honestly don't," he said. "I've got four or five names in mind. That's part of the next days' work, to check and see do the others think what I think?"

Regarding the issues the cardinals will be considering as they choose a new Pope, Cardinal Timothy Dolan, the Archbishop of New York, told CBS News that cleaning up the church after a number of scandals most likely will be part of the conclave's goal.

"Sadly, tragically, we leaders of the church have often given people reasons not to have trust in the church anymore," he said.